Question: Solve for $x$ and $y$ using elimination. ${2x-2y = -8}$ ${x-5y = -24}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-2$ ${2x-2y = -8}$ $-2x+10y = 48$ Add the top and bottom equations together. $8y = 40$ $\dfrac{8y}{{8}} = \dfrac{40}{{8}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {2x-2y = -8}\thinspace$ to find $x$ ${2x - 2}{(5)}{= -8}$ $2x-10 = -8$ $2x-10{+10} = -8{+10}$ $2x = 2$ $\dfrac{2x}{{2}} = \dfrac{2}{{2}}$ ${x = 1}$ You can also plug ${y = 5}$ into $\thinspace {x-5y = -24}\thinspace$ and get the same answer for $x$ : ${x - 5}{(5)}{= -24}$ ${x = 1}$